1. Field of the Invention
The present invention relates to a system, an apparatus, and a method for outputting PN (Pseudorandom Noise) sequences, and a data recording medium, more particularly to a system, an apparatus, and a method suitable for outputting PN sequences as spreading sequences in CDMA (Code Division Multiple Access) for spread spectrum communication which is useful for satellite communication, cable communication, mobile communication such as cellular telephony and PHS (Personal Handy phone System), and ranging such as GPS (Global Positioning System), and a data recording medium.
2. Description of the Related Art
Spread spectrum communication technology such as CDMA has employed PN sequences as spreading sequences for secure communications and efficient sharing of limited radio frequency resources.
Conventionally, the maximum length code (M-sequence), Gold code, Kasami code, and the like have been utilized to generate the PN sequences. Those code systems usually calculate the PN sequences by using linear shift register circuits and an EXCLUSIVE-OR circuit. However, it is difficult to establish secure communications because the PN sequences based on the above code system are binary sequences which are cracked easily.
The spread spectrum communication requires synchronization between communication terminals. The trade-off for enhanced security is difficulty of synchronization of the PN sequences at the receivers.
Industry has demanded a new technique for outputting PN sequences which realize more enhanced security as compared to the conventional PN sequences. Chaos theory, which is one of growth studies, has been focused on as a theory which realize more enhanced secure CDMA communications by generating hard-to-detect PN sequences.
However, chaos based PN sequences requires a receiver to search a target sequence in a huge sequence space for code synchronization. Therefore, a simple code synchronization technique has been also demanded.
The present invention has been made in consideration of the above problems. It is an object of the present invention to provide a system, an apparatus, a method for outputting PN sequences, and a data recording medium, more particularly to a system, an apparatus, a method, and a data recording medium suitable for outputting PN sequences to be utilized as spreading sequences for spread spectrum communication.
To accomplish the above objects, the following present invention will now be disclosed in accordance with the principle of the present invention.
A system for outputting pseudorandom noise sequences, based on preset elliptic function s(xe2x80xa2), a real number X (where xe2x88x921 less than X less than 1), a rational map F(xe2x80xa2,xe2x80xa2) defined by the following equation 1, and a Chebyshev map T(xe2x80xa2,xe2x80xa2) defined by the following equation 2, comprises first and second output apparatuses each having a natural number obtainer, a transmission value calculator, a transmitter, a receiver, a degree obtainer, an initial value calculator, and a sequence output unit.
In the first output apparatus,
the natural number obtainer obtains a natural number p,
the transmission value calculator calculates a value Y=F(p,X), and
the transmitter transmits the value Y to the second output apparatus.
In the second output apparatus,
the natural number obtainer obtains a natural number q,
the receiver receives the value Y transmitted by the transmitter in the first output apparatus,
the initial value calculator calculates an initial value Z=F(q,Y),
the degree obtainer obtains a degree xe2x80x9csxe2x80x9d,
the sequence output unit in the second output apparatus repeatedly applies the Chebyshev map T(s,xe2x80xa2) to the initial value Z, and outputs the following pseudorandom noise sequence having the predetermined length:
Z, T(s,Z), T(s,T(r,Z)), T(s,T(s,T(s,Z))), . . .
the transmission value calculator calculates a value Yxe2x80x2=F(q,X), and
the transmitter transmits the value Yxe2x80x2 to the first output apparatus.
In the first output apparatus,
the receiver receives the value Yxe2x80x2 transmitted by the transmitter in the second output apparatus,
the initial value calculator calculates an initial value Zxe2x80x2=F(p,Yxe2x80x2),
the degree obtainer obtains a degree xe2x80x9crxe2x80x9d, and
the sequence output unit repeatedly applies the Chebyshev map T(r,xe2x80xa2) to the initial value Zxe2x80x2, and outputs the following pseudorandom noise sequence having the predetermined length:
Zxe2x80x2, T(r,Zxe2x80x2), T(r,T(r,Zxe2x80x2)), T(r,T(r,T(r,Zxe2x80x2))), . . .                               F          ⁢                      xe2x80x83                    ⁢                      (                          n              ,                              s                ⁢                                  xe2x80x83                                ⁢                                  (                  x                  )                                                      )                          =                  s          ⁢                      xe2x80x83                    ⁢                      (            nx            )                    ⁢                      xe2x80x83                    ⁢                      (                          n              ⁢                              xe2x80x83                            ⁢                              is  a  natural  number  equal
to  or  greater  than  2                                      )                                              Equation        ⁢                  xe2x80x83                ⁢        1                                          T          ⁢                      xe2x80x83                    ⁢                      (                          n              ,                              cos                ⁢                                  xe2x80x83                                ⁢                x                                      )                          =                  cos          ⁢                      xe2x80x83                    ⁢          nx          ⁢                      xe2x80x83                    ⁢                      (                          n              ⁢                              xe2x80x83                            ⁢                              is  a  natural  number  equal
to  or  greater  than  2                                      )                                              Equation        ⁢                  xe2x80x83                ⁢        2            
The degree obtainers in the first and second output apparatuses may obtain prime numbers as the degrees.
An apparatus according to present invention outputs pseudorandom noise sequences based on preset elliptic function s(xe2x80xa2), a real number X (where xe2x88x921 less than X less than 1), a rational map F(xe2x80xa2,xe2x80xa2) defined by the following equation 1, and a Chebyshev map T(xe2x80xa2,xe2x80xa2) defined by the following equation 2.
The apparatus comprises:
a natural number obtainer which obtains a natural number p;
a transmission value calculator which calculates a value Y=F(p,X);
a transmitter which transmits the value Y to another output apparatus,
a receiver which receives a value Yxe2x80x2 transmitted by another output apparatus,
an initial value calculator which calculates an initial value Zxe2x80x2=F(p,Yxe2x80x2),
a degree obtainer which obtains a degree xe2x80x9crxe2x80x9d,
a sequence output unit which repeatedly applies the Chebyshev map T(r,xe2x80xa2) to the initial value Zxe2x80x2, and outputs the following pseudorandom noise sequence having the predetermined length;
Zxe2x80x2, T(r,Zxe2x80x2), T(r,T(r,Zxe2x80x2)), T(r,T(r,T(r,Zxe2x80x2))), . . .
The degree obtainers in the first and second output apparatuses may obtain prime numbers as the degrees.
A system according to the present invention outputs pseudorandom noise sequences, based on a preset elliptic function s(xe2x80xa2), a real number X (where xe2x88x921 less than X less than 1), a rational map F(xe2x80xa2,xe2x80xa2) defined by the following equation 1, and a Chebyshev map T(xe2x80xa2,xe2x80xa2) defined by the following equation 2, and comprises a plurality of output apparatuses.
Each of the output apparatuses comprises:
a natural number obtainer which obtains a natural number p;
a first transmission value calculator which calculates a value Y=F(p,X);
a transmitter which transmits the value Y to the other output apparatus;
a receiver which receives a value Yxe2x80x2 transmitted by the other apparatus;
a second transmission value calculator which calculates a value Yxe2x80x3=F(p,Yxe2x80x2) when a function F(p,xe2x80xa2) has not been applied to the value Yxe2x80x2;
a second transmitter which transmits the value Yxe2x80x3 to the other output apparatus;
an initial value calculator which calculates an initial value Zxe2x80x2=F(p,Yxe2x80x2) when the function F(p,xe2x80xa2) has been applied to the value Yxe2x80x2;
a degree obtainer which obtains a degree xe2x80x9crxe2x80x9d:
a sequence output unit which repeatedly applies the Chebyshev map T(r,xe2x80xa2) to the initial value Zxe2x80xa2, and outputs the following pseudorandom noise sequence having the predetermined length:
Zxe2x80x2, T(rZxe2x80x2), T(r,T(r,Zxe2x80x2)), T(r,T(r,T(r,Zxe2x80x2))), . . .
The degree obtainer in each of the output apparatuses may obtain a prime number as the degree.
The output system may be divided into a plurality of groups, and same real numbers may be input to the transmission value calculators in the output apparatuses in the same group.
An apparatus according to the present invention outputs pseudorandom noise sequences, based on preset elliptic function s(xe2x80xa2), a real number X (where xe2x88x921 less than X less than 1), a rational map F(xe2x80xa2,xe2x80xa2) defined by the following equation 1, and a Chebyshev map T(xe2x80xa2,xe2x80xa2) defined by the following equation 2.
The output apparatus comprises:
a natural number obtainer which obtains a natural number p;
a transmission value calculator which calculates a value Y=F(p,X);
a transmitter which transmits the value Yxe2x80x2 to another output apparatus,
a receiver which receives a value Yxe2x80x2 transmitted by another output apparatus,
an initial value calculator which calculates an initial value Zxe2x80x2=F(p,Yxe2x80x2),
a degree obtainer which obtains a degree xe2x80x9crxe2x80x9d,
a sequence output unit which repeatedly applies the Chebyshev map T(xe2x80xa2, xe2x80xa2) to the value Zxe2x80x2, and outputs the following pseudorandom noise sequence having the etermined length:
Zxe2x80x2, T(r,Zxe2x80x2), T(r,T(r,Zxe2x80x2)), T(r,T(r,T(r,Zxe2x80x2))), . . .
The degree obtainer may obtain a prime number as the degree.
A method according to the present invention outputs pseudorandom noise sequences based on a preset elliptic function s(xe2x80xa2), a real number X (where xe2x88x921 less than X less than 1), a rational map F(xe2x80xa2,xe2x80xa2) defined by the following equation 1, and a Chebyshev map T(xe2x80xa2,xe2x80xa2) defined by the lowing equation 2.
The method comprises:
obtaining a natural number p;
calculating a value Y=F(p,X);
transmitting the value Y;
receiving a value Yxe2x80x2;
calculating an initial value Zxe2x80x2=F(p,Yxe2x80x2);
obtaining a degree xe2x80x9crxe2x80x9d; and
repeatedly applying a Chebyshev map T(xe2x80xa2,xe2x80xa2) to the initial value Zxe2x80x2, and outputting the following pseudorandom noise sequence having the predetermined length:
Zxe2x80x2, T(r,Zxe2x80x2), T(r,T(r,Zxe2x80x2)), T(r,T(r,T(r,Zxe2x80x2))), . . .
The obtaining the degree may obtain a prime number as the degree.
A method according to the present invention outputs pseudorandom noise sequences based on a preset elliptic function s(xe2x80xa2), a real number X (where xe2x88x921 less than X less than 1), a rational map F(xe2x80xa2,xe2x80xa2) defined by the following equation 1, and a Chebyshev map T(xe2x80xa2,xe2x80xa2) defined by the following equation.
The method comprises:
obtaining a natural number p;
calculating a value Y=F(p,X) based on the obtained natural number p;
transmitting the value Y;
receiving a value Yxe2x80x2;
calculating a value Yxe2x80x3=F(p,Yxe2x80x2) when a function F(p,xe2x80xa2) has not been applied to the value Yxe2x80x2;
transmits the value Yxe2x80x3;
calculating an initial value Zxe2x80x2=F(p,Yxe2x80x2) when the function F(p,xe2x80xa2) has been applied to the value Yxe2x80x2;
obtaining a degree xe2x80x9crxe2x80x9d:
repeatedly applying the Chebyshev map T(r,xe2x80xa2) to the initial value Zxe2x80x2, and outputting the following pseudorandom noise sequence having the predetermined length:
Zxe2x80x2, T(r,Zxe2x80x2), T(r,T(r,Zxe2x80x2)), T(r,T(r,T(r,Zxe2x80x2))), . . .
The obtaining the degree may obtain a prime number as the degree.
A program which realizes the system, the apparatus, and the method for outputting the pseudorandom noise sequences may be stored in a data recording medium such as a compact disc, a floppy disk, a hard disk, an magneto-optical disk, a digital versatile disc, a magnetic tape, and a semiconductor memory.
Executing the program stored in the data recording medium according to the present invention by a data processor such as a general purpose computer or a parallel computer which comprises a storage device, a calculator, an output device, and the like realizes the system, the apparatus, and the method for outputting the pseudorandom noise sequences.
The data recording medium storing the program according to the present invention may be distributed or merchandized as a single product independent from the data processor.